4,362 research outputs found
The Ising spin glass in finite dimensions: a perturbative study of the free energy
Replica field theory is used to study the n-dependent free energy of the
Ising spin glass in a first order perturbative treatment. Large
sample-to-sample deviations of the free energy from its quenched average prove
to be Gaussian, independently of the special structure of the order parameter.
The free energy difference between the replica symmetric and (infinite level)
replica symmetry broken phases is studied in details: the line n(T) where it is
zero coincides with the Almeida-Thouless line for d>8. The dimensional domain
6<d<8 is more complicated, and several scenarios are possible.Comment: 23 page
Concentrated rural poverty and the geography of exclusion
One-half of rural poor are segregated in high-poverty areas, a new policy brief co-published by the Carsey Institute at the University of New Hampshire and Rural Realities. This brief highlights the challenges faced by America\u27s rural poor, particularly as they are physically and socially isolated from middle-class communities that might offer economic opportunities
The Glassy Potts Model
We introduce a Potts model with quenched, frustrated disorder, that enjoys of
a gauge symmetry that forbids spontaneous magnetization, and allows the glassy
phase to extend from down to T=0. We study numerical the 4 dimensional
model with states. We show the existence of a glassy phase, and we
characterize it by studying the probability distributions of an order
parameter, the binder cumulant and the divergence of the overlap
susceptibility. We show that the dynamical behavior of the system is
characterized by aging.Comment: 4 pages including 4 (color) ps figures (all on page 4
1-loop contribution to the dynamical exponents in spin glasses
We evaluate the corrections to the mean field values of the and the
exponents at the first order in the -expansion, for . We find
that both and are decreasing when the space dimension decreases.Comment: 12 pages 3 Postscript figure
Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
In this work we analyse the Parisi's infinity-replica symmetry breaking
solution of the Sherrington - Kirkpatrick model without external field using
high order perturbative expansions. The predictions are compared with those
obtained from the numerical solution of the infinity-replica symmetry breaking
equations which are solved using a new pseudo-spectral code which allows for
very accurate results. With this methods we are able to get more insight into
the analytical properties of the solutions. We are also able to determine
numerically the end-point x_{max} of the plateau of q(x) and find that lim_{T
--> 0} x_{max}(T) > 0.5.Comment: 15 pages, 11 figures, RevTeX 4.
Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation
A careful critical analysis of the complexity, at the annealed level, of the
Sherrington-Kirkpatrick model has been performed. The complexity functional is
proved to be always invariant under the Becchi-Rouet-Stora-Tyutin
supersymmetry, disregarding the formulation used to define it. We consider two
different saddle points of such functional, one satisfying the supersymmetry
[A. Cavagna {\it et al.}, J. Phys. A {\bf 36} (2003) 1175] and the other one
breaking it [A.J. Bray and M.A. Moore, J. Phys. C {\bf 13} (1980) L469]. We
review the previews studies on the subject, linking different perspectives and
pointing out some inadequacies and even inconsistencies in both solutions.Comment: 20 pages, 4 figure
On Spin-Glass Complexity
We study the quenched complexity in spin-glass mean-field models satisfying
the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study,
consistent with recent numerical results, allows, in principle, to conjecture
the absence of any supersymmetric contribution to the complexity in the
Sherrington-Kirkpatrick model. The same analysis can be applied to any model
with a Full Replica Symmetry Breaking phase, e.g. the Ising -spin model
below the Gardner temperature. The existence of different solutions, breaking
the supersymmetry, is also discussed.Comment: 4 pages, 2 figures; Text changed in some parts, typos corrected,
Refs. [17],[21] and [22] added, two Refs. remove
Dynamical critical exponents for the mean-field Potts glass
In this paper we study the critical behaviour of the fully-connected
p-colours Potts model at the dynamical transition. In the framework of Mode
Coupling Theory (MCT), the time autocorrelation function displays a two step
relaxation, with two exponents governing the approach to the plateau and the
exit from it. Exploiting a relation between statics and equilibrium dynamics
which has been recently introduced, we are able to compute the critical slowing
down exponents at the dynamical transition with arbitrary precision and for any
value of the number of colours p. When available, we compare our exact results
with numerical simulations. In addition, we present a detailed study of the
dynamical transition in the large p limit, showing that the system is not
equivalent to a random energy model.Comment: 10 pages, 3 figure
Renormalons in the effective potential of the vectorial model
We study the properties of ultraviolet renormalons in the vectorial
model. This is achieved by studying the effective
potential of the theory at next to leading order of the expansion, the
appearence ofthe renormalons in the perturbative series and their relation to
the imaginary part of the potential. We also consider the mechanism of
renormalon cancellation by `irrelevant" higher dimensional operators.Comment: 20 pages, Latex, 3 Postscript figure
Replica analysis of partition-function zeros in spin-glass models
We study the partition-function zeros in mean-field spin-glass models. We
show that the replica method is useful to find the locations of zeros in a
complex parameter plane. For the random energy model, we obtain the phase
diagram in the plane and find that there are two types of distribution of
zeros: two-dimensional distribution within a phase and one-dimensional one on a
phase boundary. Phases with a two-dimensional distribution are characterized by
a novel order parameter defined in the present replica analysis. We also
discuss possible patterns of distributions by studying several systems.Comment: 23 pages, 12 figures; minor change
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